Tetracot comma - Revision history

ArrowHead294 at 01:55, 4 December 2024

2024-12-04T01:55:30Z

← Older revision		Revision as of 01:55, 4 December 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''tetracot comma''' ({{monzo\|legend=1\| 5 -9 4 }}, [[ratio]]: 20000/19683), or '''minimal diesis''', is a [[small comma\|small]] [[5-limit]] [[comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a [[3/2\|fifth]]; that is, (10/9)<sup>4</sup>/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4\|just major thirds]] and nine just perfect fifths, which directly follows from its monzo. Another characterization is the interval between four [[81/80\|syntonic commas]] and a [[2187/2048\|Pythagorean apotome]], making the corresponding temperament a member of the [[syntonic-chromatic equivalence continuum]]. Since an apotome minus two syntonic commas is a [[25/24\|classical chroma]], the comma can be expressed as the difference between an apotome and a stack of two classical chromas, or between a classical chroma and a stack of two syntonic commas.		The '''tetracot comma''' ({{monzo\|legend=1\| 5 -9 4 }}, [[ratio]]: 20000/19683), or '''minimal diesis''', is a [[small comma\|small]] [[5-limit]] [[comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a [[3/2\|fifth]]; that is, (10/9)<sup>4</sup>/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4\|just major thirds]] and nine just perfect fifths, which directly follows from its monzo. Another characterization is the interval between four [[81/80\|syntonic commas]] and a [[2187/2048\|Pythagorean apotome]], making the corresponding temperament a member of the [[syntonic–chromatic equivalence continuum]]. Since an apotome minus two syntonic commas is a [[25/24\|classical chroma]], the comma can be expressed as the difference between an apotome and a stack of two classical chromas, or between a classical chroma and a stack of two syntonic commas.

	== Temperaments ==		== Temperaments ==

FloraC: Rework

2024-11-12T15:20:26Z

Rework

← Older revision		Revision as of 15:20, 12 November 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	~~'''20000/19683''', the~~ '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a [[3/2\|fifth]]; that is, (10/9)^4/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4\|just major thirds]] and nine just perfect fifths, between four [[81/80\|syntonic commas]] and a [[2187/2048\|Pythagorean apotome]], ~~or between~~ two syntonic commas ~~and~~ a [[25/24\|~~classic chromatic semitone~~]]. Tempering it out leads to the [[tetracot family]] of temperaments.		The '''tetracot comma''' ({{monzo\|legend=1\| 5 -9 4 }}, [[ratio]]: 20000/19683), or '''minimal diesis''', is a [[small comma\|small]] [[5-limit]] [[comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a [[3/2\|fifth]]; that is, (10/9)<sup>4</sup>/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4\|just major thirds]] and nine just perfect fifths, which directly follows from its monzo. Another characterization is the interval between four [[81/80\|syntonic commas]] and a [[2187/2048\|Pythagorean apotome]], making the corresponding temperament a member of the [[syntonic-chromatic equivalence continuum]]. Since an apotome minus two syntonic commas is a [[25/24\|classical chroma]], the comma can be expressed as the difference between an apotome and a stack of two classical chromas, or between a classical chroma and a stack of two syntonic commas.

			== Temperaments ==
			Tempering out this comma leads to the [[tetracot family]] of temperaments.

	[[Category:Tetracot]]		[[Category:Tetracot]]
	[[Category:Commas named for how they divide the fifth]]		[[Category:Commas named for how they divide the fifth]]

BudjarnLambeth at 00:45, 4 November 2024

2024-11-04T00:45:07Z

← Older revision		Revision as of 00:45, 4 November 2024
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	[[Category:Tetracot]]		[[Category:Tetracot]]
	[[Category:Commas named for ~~their regular temperament properties~~]]		[[Category:Commas named for how they divide the fifth]]

BudjarnLambeth at 09:00, 3 November 2024

2024-11-03T09:00:51Z

← Older revision		Revision as of 09:00, 3 November 2024
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	[[Category:Tetracot]]		[[Category:Tetracot]]
			[[Category:Commas named for their regular temperament properties]]

ArrowHead294 at 13:55, 21 September 2024

2024-09-21T13:55:02Z

← Older revision		Revision as of 13:55, 21 September 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''20000/19683''', the '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a [[3/2\|fifth]]; that is, (10/9)^4/(3/2). It can also be expressed as the ~~amount by which an~~ octave-reduced ~~stack of~~ four [[5/4\|just major thirds]] ~~exceeds an octave-reduced stack of~~ nine fifths, ~~or as the difference~~ between ~~two~~ [[81/80\|syntonic commas]] and a [[25/24\|classic chromatic semitone]]. Tempering it out leads to the [[tetracot family]] of temperaments.		'''20000/19683''', the '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a [[3/2\|fifth]]; that is, (10/9)^4/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4\|just major thirds]] and nine just perfect fifths, between four [[81/80\|syntonic commas]] and a [[2187/2048\|Pythagorean apotome]], or between two syntonic commas and a [[25/24\|classic chromatic semitone]]. Tempering it out leads to the [[tetracot family]] of temperaments.

	[[Category:~~tetracot~~]]		[[Category:Tetracot]]

ArrowHead294 at 12:00, 8 July 2024

2024-07-08T12:00:25Z

← Older revision		Revision as of 12:00, 8 July 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''20000/19683''', the '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a [[3/2\|fifth]]; that is, (10/9)^4/(3/2). It can also be expressed as the amount by which an octave-reduced stack of four [[5/4\|just major thirds]] exceeds an octave-reduced stack of nine fifths. Tempering it out leads to the [[tetracot family]] of temperaments.		'''20000/19683''', the '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a [[3/2\|fifth]]; that is, (10/9)^4/(3/2). It can also be expressed as the amount by which an octave-reduced stack of four [[5/4\|just major thirds]] exceeds an octave-reduced stack of nine fifths, or as the difference between two [[81/80\|syntonic commas]] and a [[25/24\|classic chromatic semitone]]. Tempering it out leads to the [[tetracot family]] of temperaments.

	[[Category:tetracot]]		[[Category:tetracot]]

Lucius Chiaraviglio: Add relation of major thirds to fifths.

2024-06-21T08:30:40Z

Add relation of major thirds to fifths.

← Older revision		Revision as of 08:30, 21 June 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''20000/19683''', the '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a fifth; that is, (10/9)^4/(3/2). Tempering it out leads to the [[tetracot family]] of temperaments.		'''20000/19683''', the '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a [[3/2\|fifth]]; that is, (10/9)^4/(3/2). It can also be expressed as the amount by which an octave-reduced stack of four [[5/4\|just major thirds]] exceeds an octave-reduced stack of nine fifths. Tempering it out leads to the [[tetracot family]] of temperaments.

	[[Category:tetracot]]		[[Category:tetracot]]

TallKite: added color name

2022-12-04T02:19:51Z

added color name

← Older revision		Revision as of 02:19, 4 December 2022
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	\| Ratio = 20000/19683		\| Ratio = 20000/19683
	\| Name = tetracot comma, minimal diesis		\| Name = tetracot comma, minimal diesis
			\| Color name = sy<sup>4</sup>1, Saquadyo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Infobox Interval added

2022-10-27T16:17:46Z

Infobox Interval added

← Older revision		Revision as of 16:17, 27 October 2022
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			{{Infobox Interval
			\| Ratio = 20000/19683
			\| Name = tetracot comma, minimal diesis
			\| Comma = yes
			}}
	'''20000/19683''', the '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a fifth; that is, (10/9)^4/(3/2). Tempering it out leads to the [[tetracot family]] of temperaments.		'''20000/19683''', the '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9\|minor whole tones]] exceed a fifth; that is, (10/9)^4/(3/2). Tempering it out leads to the [[tetracot family]] of temperaments.

	~~[[Category:5-limit]]~~
	~~[[Category:Small commas]]~~
	[[Category:tetracot]]		[[Category:tetracot]]

Fredg999 category edits: Moving from Category:Small comma to Category:Small commas using Cat-a-lot

2022-03-20T22:00:00Z

Moving from Category:Small comma to Category:Small commas using Cat-a-lot

← Older revision		Revision as of 22:00, 20 March 2022
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	[[Category:5-limit]]		[[Category:5-limit]]
	[[Category:Small ~~comma~~]]		[[Category:Small commas]]
	[[Category:tetracot]]		[[Category:tetracot]]